More Efficient Secret-Shared Joins with Multiplicity via Oblivious Sort Expansion

Secret-shared SQL-style join is a fundamental building block in secure collaborative data analysis. In practice, join operations frequently involve duplicate keys, giving rise to one-to-many (Join-OM) and many-to-many (Join-MM) relationships. Supporting such joins requires obliviously materializing all matching row pairs. Existing protocols achieve this in two costly ways: they either perform oblivious sorting over a larger expanded input or rely on multiple aggregation trees that incur additional logarithmic rounds.

In this work, we present highly efficient protocols for Join-OM and Join-MM over secret-shared databases in the standard semi-honest setting. Our core contribution is Oblivious Sort Expansion (OSE), a novel constant-round protocol that may be of independent interest. Rather than obliviously sorting the expanded input from scratch, we sort only the original input and use OSE to derive the sorted order after expansion. For Join-OM, OSE eliminates the redundant sorting overhead introduced by input expansion in the state-of-the-art protocol by Asharov et al. (CCS 2023). For Join-MM, we combine OSE with local linear operations to obtain an aggregation-tree-free Join-MM protocol. Experimental results show that our protocols consistently outperform prior protocols, reducing both runtime and communication costs by approximately $27\%$ and $65\%$ for Join-OM and Join-MM, respectively.